The problem I'm working on is for a boundary layer equation for an aerodynamics problem. But I'm having issues working out the partials for it, its been a long while since I've done them and I'm just not getting it to work out. Now for the problem.

I have functions:

where

is

I need to find the following partials for my problem:

,

,

,

,

,

,

,

The second order are the ones I know I'm totally missing, the others I may be getting but it'd be nice to get a sanity check. The ones in terms of

and x may cancel out when it goes back into my aerodynamics but I'm not positive of that yet.

Thanks for any help, believe me I've given this problem a solid 14 hours of head bashing yesterday before asking for help.